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arXiv 1602.01622hep-phnucl-thphysics.flu-dyn
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耗散相对论等离子体各向异性不稳定性的流体动力学研究

A Hydrodynamic Approach to the Study of Anisotropic Instabilities in Dissipative Relativistic Plasmas

Esteban Calzetta, Alejandra Kandus

备注：
13 pages. Three figures. The analysis of the instabilities was improved in order to compare our results with the ones in the literature. The motivation for developing a pure hydrodynamic formalism is clarified, the meaning of the different equations and tensors is explained. Typos and misplaced references were corrected. Uses revtex. Accepted for publication in Int. Jour. of Mod. Phys. A
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摘要：

我们开发了一个纯粹的流体动力学的形式主义来描述碰撞，各向异性不稳定性的相对论等离子体，通常描述与动力学理论工具。我们的主要动机是这样一个事实，即粗粒模型的高粒子数系统提供更清晰和全面的物理描述这些系统比纯粹的动力学方法，可以更容易地测试实验以及数值。特别是，我们的目标是开发一个理论，描述了一个背景的非平衡流体配置和它的扰动，能够占后者对前者的反作用。我们的方程组包括能量动量张量和电流的通常守恒定律，以及两个新的张量方程，它们编码了耗散信息。为了与动力学理论联系起来，我们将不同的张量写成非平衡单粒子分布函数（1 pdf）的矩，为了说明的目的，我们采用类似梯度的形式。虽然这种选择限制了形式主义对离平衡不远的状态的适用性，但它保留了基本动力学理论的主要特征。我们假设Vlasov-Boltzmann方程的有效性，与Anderson-Witting处方，这是更适合于高度相对论性系统比Marle的（或Bhatnagar，Gross和Krook）的形式给出的碰撞积分，并推导出守恒律采取相应的时刻。我们应用我们的发展来研究各向异性，但轴对称的背景下出现的不稳定性。对于小偏差的各向同性，我们发现正常模式的色散关系，这承认不稳定的解决方案的参数空间的值范围很广。

英文摘要：

We develop a purely hydrodynamic formalism to describe collisional, anisotropic instabilities in a relativistic plasma, that are usually described with kinetic theory tools. Our main motivation is the fact that coarse-grained models of high particle number systems give more clear and comprehensive physical descriptions of those systems than purely kinetic approaches, and can be more easily tested experimentally as well as numerically. In particular, we aim at developing a theory that describes both a background non-equilibrium fluid configurations and its perturbations, to be able to account for the backreaction of the latter on the former. Our system of equations includes the usual conservation laws for the energy-momentum tensor and for the electric current, and the equations for two new tensors that encode the information about dissipation. To make contact with kinetic theory, we write the different tensors as the moments of a non-equilibrium one-particle distribution function (1pdf) which, for illustrative purposes, we take in the form of a Grad-like ansatz. Although this choice limits the applicability of the formalism to states not far from equilibrium, it retains the main features of the underlying kinetic theory. We assume the validity of the Vlasov-Boltzmann equation, with a collision integral given by the Anderson-Witting prescription, which is more suitable for highly relativistic systems than Marle's (or Bhatnagar, Gross and Krook) form, and derive the conservation laws by taking its corresponding moments. We apply our developments to study the emergence of instabilities in an anisotropic, but axially symmetric background. For small departures of isotropy we find the dispersion relation for normal modes, which admit unstable solutions for a wide range of values of the parameter space.

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